Respostas

2014-06-11T11:19:57-03:00
log_{6} 4=alog_{6}  2^{2} =a2.log_{6}  2 =alog_{6}  2 = \frac{a}{2}  \frac{log_{3} 2}{log_{3} 6} =\frac{log_{3} 2}{log_{3} 2.3} =\frac{log_{3} 2}{log_{3} 2+log_{3} 3}=\frac{log_{3} 2}{log_{3} 2+1}= \frac{a}{2}

Façamos log_{3} 2=x\frac{x}{x+1}= \frac{a}{2}2x=ax+a2x-ax=a(2-a).x=ax= \frac{a}{2-a}

Logo: log_{3} 2=\frac{a}{2-a}

log_{9} 32=log_{9}  2^{5} =5log_{9} 2=

=5. \frac{log_{3} 2}{log_{3}  3^{2} } =5. \frac{log_{3} 2}{2.log_{3}  3 }  =5. \frac{log_{3} 2}{2.1 } = \frac{5}{2} .log_{3} 2=\frac{5}{2} .(\frac{a}{2-a})=\frac{5a}{4-2a}
2 5 2